Quadratic equation x2-k-x equals 0

Answer 1

2

Answer 2

The equation x^2-x-k=0 is the equation of a parabola. Let k=0 for example and we have x^2-x=0 or x(x-1)=0 This is a parabola with x intercepts at 0 and 1. The y intercept is 0 as well. Look at x^2-x-1=0 This does not factor over the integers but it does factor over the real numbers as (2x+Squareroot(5)-1)(2x-Squareroot(5)-1) so let each quantity in the product equal 0 and find the x intercepts of the parabola. In general ax^2+bx+c=0 is a quadratic equation if a is not 0. The graph of this equation is a parabola as can be easily proved. The quadratic you gave is a special case of this where b=-1 and c=-k